Related papers: Machine Learning Framework for Efficient Predictio…

Understanding the theoretical capabilities and limitations of quantum machine learning (QML) models to solve machine learning tasks is crucial to advancing both quantum software and hardware developments. Similarly to the classical setting,…

We propose a new unsupervised anomaly detection method based on the sliced-Wasserstein distance for training data selection in machine learning approaches. Our filtering technique is interesting for decision-making pipelines deploying…

1. Complex systems of moving and interacting objects are ubiquitous in the natural and social sciences. Predicting their behavior often requires models that mimic these systems with sufficient accuracy, while accounting for their inherent…

The autocovariance and cross-covariance functions naturally appear in many time series procedures (e.g., autoregression or prediction). Under assumptions, empirical versions of the autocovariance and cross-covariance are asymptotically…

This work characterizes, analytically and numerically, two major effects of the quadratic Wasserstein ($W_2$) distance as the measure of data discrepancy in computational solutions of inverse problems. First, we show, in the…

In quantum information, trace distance is a basic metric of distinguishability between quantum states. However, there is no known efficient approach to estimate the value of trace distance in general. In this paper, we propose efficient…

In this work we test Wasserstein distance in conjunction with persistent homology, as a tool for discriminating large scale structures of simulated universes with different values of $\sigma_8$ cosmological parameter (present…

Quantum metrology is a general term for methods to precisely estimate the value of an unknown parameter by actively using quantum resources. In particular, some classes of entangled states can be used to significantly suppress the…

Consider a set of points sampled independently near a smooth compact submanifold of Euclidean space. We provide mathematically rigorous bounds on the number of sample points required to estimate both the dimension and the tangent spaces of…

We propose a generalization of the Wasserstein distance of order 1 to the quantum states of $n$ qudits. The proposal recovers the Hamming distance for the vectors of the canonical basis, and more generally the classical Wasserstein distance…

We consider $M/Ph/n+M$ queueing systems in steady state. We prove that the Wasserstein distance between the stationary distribution of the normalized system size process and that of a piecewise Ornstein-Uhlenbeck (OU) process is bounded by…

Quantum computers promise to enhance machine learning for practical applications. Quantum machine learning for real-world data has to handle extensive amounts of high-dimensional data. However, conventional methods for measuring quantum…

High-fidelity measurements are important for the physical implementation of quantum information protocols. Current methods for classifying measurement trajectories in superconducting qubit systems produce fidelities that are systematically…

Despite of its importance for safe machine learning, uncertainty quantification for neural networks is far from being solved. State-of-the-art approaches to estimate neural uncertainties are often hybrid, combining parametric models with…

Many machine learning problems can be expressed as the optimization of some cost functional over a parametric family of probability distributions. It is often beneficial to solve such optimization problems using natural gradient methods.…

Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…

We introduce the Wasserstein Transform (WT), a general unsupervised framework for updating distance structures on given data sets with the purpose of enhancing features and denoising. Our framework represents each data point by a…

This paper presents a distributionally robust Q-Learning algorithm (DrQ) which leverages Wasserstein ambiguity sets to provide idealistic probabilistic out-of-sample safety guarantees during online learning. First, we follow past work by…

We present a novel $Q$-learning algorithm tailored to solve distributionally robust Markov decision problems where the corresponding ambiguity set of transition probabilities for the underlying Markov decision process is a Wasserstein ball…

The emergence of time-series foundation model research elevates the growing need to measure the (dis)similarity of time-series datasets. A time-series dataset similarity measure aids research in multiple ways, including model selection,…